Conformal Manifolds in Four Dimensions and Chiral Algebras

Abstract

Any N=2 superconformal field theory (SCFT) in four dimensions has a sector of operators related to a two-dimensional chiral algebra containing a Virasoro sub-algebra. Moreover, there are well-known examples of isolated SCFTs whose chiral algebra is a Virasoro algebra. In this note, we consider the chiral algebras associated with interacting N=2 SCFTs possessing an exactly marginal deformation that can be interpreted as a gauge coupling (i.e., at special points on the resulting conformal manifolds, free gauge fields appear that decouple from isolated SCFT building blocks). At any point on these conformal manifolds, we argue that the associated chiral algebras possess at least three generators. In addition, we show that there are examples of SCFTs realizing such a minimal chiral algebra: they are certain points on the conformal manifold obtained by considering the low-energy limit of type IIB string theory on the three complex-dimensional hypersurface singularity x_1^3+x_2^3+x_3^3+A x_1x_2x_3+w^2=0. The associated chiral algebra is the A(6) theory of Feigin, Feigin, and Tipunin. As byproducts of our work, we argue that (i) a collection of isolated theories can be conformally gauged only if there is a SUSY moduli space associated with the corresponding symmetry current moment maps in each sector, and (ii) N=2 SCFTs with a>=c have hidden fermionic symmetries (in the sense of fermionic chiral algebra generators).

25 pages and 1 figure; v2: minor improvements in discussion; results unchanged

References in corpus (10)

• R-Twisting and 4d/2d Correspondences
• Cardy Formulae for SUSY Theories in d=4 and d=6
• A holographic computation of the central charges of d=4, N=2 SCFTs
• High-temperature asymptotics of supersymmetric partition functions
• On 4d rank-one N=3 superconformal field theories
• Tri-vertices and SU(2)'s
• Argyres-Douglas Theories and S-Duality
• A search for minimal 4d N=1 SCFT
• A Small Deformation of a Simple Theory
• Characters of coinvariants in (1,p) logarithmic models

Cited by in corpus (35)

• Vertex operator algebras, Higgs branches, and modular differential equations
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• Surface Defects and Chiral Algebras
• Vertex operator algebras of Argyres-Douglas theories from M5-branes
• Chiral algebra of Argyres-Douglas theory from M5 brane
• New aspects of Argyres--Douglas theories and their dimensional reduction
• On Irregular Singularity Wave Functions and Superconformal Indices
• Macdonald Index and Chiral Algebra
• Logarithmic W-algebras and Argyres-Douglas theories at higher rank
• 1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds
• Schur correlation functions on $S^3\times S^1$
• Nonunitary Lagrangians and unitary non-Lagrangian conformal field theories
• A slow review of the AGT correspondence
• Surface Defect Indices and 2d-4d BPS States
• $\mathcal{N}=2^{\ast }$ Schur indices
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• Conformal Manifolds and 3d Mirrors of Argyres-Douglas theories
• Schur sector of Argyres-Douglas theory and $W$-algebra
• Braided Tensor Categories related to ${\mathcal{B}}_p$ Vertex Algebras
• Rationalizing CFTs and Anyonic Imprints on Higgs Branches
• On the chiral algebra of Argyres-Douglas theories and S-duality
• On the Correspondence between Surface Operators in Argyres-Douglas Theories and Modules of Chiral Algebra
• Vanishing OPE Coefficients in 4d N=2 SCFTs
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Infinitely many 4d N=1 SCFTs with a=c
• OPE Selection Rules for Schur Multiplets in 4D $\mathcal{N}=2$ Superconformal Field Theories
• A tale of 2-groups: D${}_p$(USp(2N)) theories
• The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory
• 4d/2d $\to$ 3d/1d: A song of protected operator algebras
• Representation theory of W-algebras and Higgs branch conjecture
• W algebra, Cosets and VOA for 4d N = 2 SCFT from M5 branes
• Associated varieties and Higgs branches (a survey)
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• 4d $\mathcal{N}=2$ SCFTs and lisse W-algebras
• Vanishing short multiplets in rank one 4d/5d SCFTs